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    A curious matrix-sum identity and certain finite sums identities
    (World Scientific Publ Co Pte Ltd, 2015) Kilic, Emrah; Akkus, Ilker; Omur, Nese; Ulutas, Yucel T.
    In this paper, we consider two generalized binary sequences and then give a generalization of a matrix equality proposed as an advanced problem. Then, we derive new certain finite sums including the generalized binary sequences as applications.
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    Diophantine Equations Related with Linear Binary Recurrences
    (Tarbiat Modares Univ, Acecr, 2022) Kilic, Emrah; Akkus, Ilker; Omur, Nese
    In this paper we find all solutions of four kinds of the Dio-phantine equations x(2) +/- V(t)xy - y(2) +/- x = 0 and x(2) +/- V(t)xy - y(2) +/- y = 0, for an odd number t, and, x(2) +/- V(t)xy + y(2) - x = 0 and x(2) +/- V(t)xy +/- y(2) - y = 0, for an even number t, where V-n is a generalized Lucas number. This paper continues and extends a previous work of Bahramian and Daghigh.
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    Formulas for binomial sums including powers of Fibonacci and Lucas numbers
    (Univ Politehnica Bucharest, Sci Bull, 2015) Kilic, Emrah; Akkus, Ilker; Omur, Nese; Ulutas, Yucel Turker
    Recently Prodinger [2] proved general expansion formulas for sums of powers of Fibonacci and Lucas numbers. In this paper, we will prove general expansion formulas for binomial sums of powers of Fibonacci and Lucas numbers.
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    Generalized Binomial Convolution of the mth Powers of the Consecutive Integers with the General Fibonacci Sequence
    (De Gruyter Open Ltd, 2016) Kilic, Emrah; Akkus, Ilker; Omur, Nese; Ulutas, Yucel T.
    In this paper, we consider Gauthier's generalized convolution and then define its binomial analogue as well as alternating binomial analogue. We formulate these convolutions and give some applications of them.